Cryptology ePrint Archive: Report 2010/512

Abstract: Secure computation of the set intersection functionality allows $n$
parties to find the intersection between their datasets without
revealing anything else about them. An efficient protocol for such
task could have multiple potential applications, in commerce,
health-care, and security. However, all currently known secure set
intersection protocols for $n>2$ parties have computational costs that
are quadratic in the (maximum) number of entries in the dataset
contributed by each party, rendering secure computation of set
intersection impractical on anything but small datasets.

In this paper we describe the first multi-party protocol for securely
computing the set intersection functionality with both the
communication and the computation costs that are quasi-linear in the
size of the datasets. Specifically, our protocols require
$O(n^2k\lambda)$ bits of communication and $\tilde{O}(n^2\lambda+(n\lambda+n^2)k)$ group
multiplications per player in the malicious adversary setting, where
$k$ is the size of each dataset and $\lambda$ is security
parameter. Our protocol follows the basic idea of the protocol
proposed by Kissner and Song, but we gain efficiency by
using different representation of the polynomials associated with
users' datasets, and careful employment of algorithms that interpolate
or evaluate polynomials on multiple points more efficiently.